模具設(shè)計(jì)外文翻譯--注射／壓縮流體組合模塑的數(shù)值模擬

1、<p>　　附錄二：外文翻譯原件及翻譯稿</p><p>　　Numerical simulation of injection/compression liquid composite molding</p><p>　　Part 1. Mesh generation</p><p>　　K.M. Pillaia, C.L. Tucker III, F.

2、Ra. Phelan Jrb</p><p>　　aDepartment of Mechanical and Industrial Engineering, University of Illinois,</p><p>　　1206 W. Green Street, Urbana, IL 61801, USA</p><p>　　bPolymer Composit

3、es Group, Polymers Division, Building 224, Room B108, National Institute of</p><p>　　Standards and Technology, Gaithersburg, MD 20899, USA</p><p>　　Accepted 14 June 1999</p><p>　　──

4、─────────────────────────────────────</p><p><b>　　Abstract</b></p><p>　　This paper presents a numerical simulation of injection/compression liquid composite molding, where the fiber

5、preform is compressed to a desired degree after an initial charge of resin has been injected into the mold. Due to the possibility of an initial gap at the top of the preform and out-of-plane heterogeneity in the multi-l

6、ayered fiber preform, a full three-dimensional (3D) flow simulation is essential. We propose an algorithm to generate a suitable 3D finite element mesh, starting from a t</p><p>　　Keywords: Liquid composite

7、molding (LCM); E. Resin transfer molding (RTM)</p><p>　　───────────────────────────────────────</p><p>　　1. Introduction</p><p>　　Liquid composite molding (LCM) is emerging as an im

8、portant technology to make net-shape parts of polymer-matrix composites. In any LCM process, a preform of reinforcing fibers is placed in a closed mold, then a liquid polymer resin is injected into the mold to infiltrate

9、 the preform. When the mold is full, the polymer is cured by a crosslinking reaction to become a rigid solid. Then the mold is opened to remove the part. LCM processes offer a way to produce high-performance composite pa

10、rts using</p><p>　　This paper deals with a particular type of LCM process called injection/compression liquid composite molding (I/C-LCM). In I/C-LCM, unlike other types of LCM processes, the mold is only pa

11、rtially closed when resin injection begins. This increases the cross-sectional area available for the resin flow, and decreases flow resistance by providing high porosity in the reinforcement. Often, the presence of a ga

12、p at the top of the preform further facilitates the flow. After all of the resin has been in</p><p>　　Complete filling of the mold with adequate wetting of the fibers is the primary objective of any LCM mold

13、 designer; incomplete filling in the mold leads to production of defective parts with dry spots. There are many factors which affect the filling of the mold: permeability of the preform, presence of gaps in the mold to f

14、acilitate resin flow, arrangement of inlet and outlet gates, injection rates of resin from different inlet ports, etc. Often it is not possible for the mold designer to visual</p><p>　　I/C-LCM fiber preforms

15、 frequently comprise layers of different reinforcing materials such as biaxial woven fabrics, stitch-bonded uniaxial fibers, random fibers. Each type of material has a unique behavior as it is compressed in the mold. Whe

16、n such different materials are layered to form the preform, each of them will compress by different amounts as the mold is closed. This behavior is illustrated in Fig. 1, which shows a small piece of a mold. Here the lig

17、hter center layer deforms much more th</p><p>　　(B) After compression (A) Before compression</p><p>　　Fig. 1. Uneven deformation of preform layers under compression.</p><p>　

18、　Capturing this deformation behavior during compression is critical to the accuracy of any I/C-LCM process model. Resin flows through the preform at all stages of compression, and the porosity and permeability of the pre

19、form are critical in determining the resin flow. The ratio of deformed volume to initial volume determines the porosity of each preform layer, and from this one can determine the layer's permeability, either from a t

20、heoretical prediction or a correlation of experimental data. Beca</p><p>　　Significant steps have already been taken to computationally model the mold filling in the I/C-LCM process. A computer program calle

21、d crimson, is capable of isothermal mold filling simulation which involves simultaneous fluid flow and preform compression computations in the flow domain. But the initial capacity of crimson is limited to two-dimensiona

22、l (2D) planar geometries where prediction of preform compression is straightforward. Deformation of the preform is modeled using the incremental lin</p><p>　　Most injection molding simulation programs read f

23、or the mold geometry in the form of a shell mesh. Even if it were possible to transmit the full geometrical information about the mold through a 3D mesh, it still is difficult to incorporate all the information of releva

24、nce to the process engineer. The latter needs to know the thicknesses of various layers of fiber mats and their corresponding porosities at each time step. As a result, it is very important that elements representing dif

25、ferent laye</p><p>　　The objectives of this paper are to introduce basic ideas about modeling mold filling in 3D I/C-LCM parts, and to introduce an algorithm to generate a 3D finite element mesh from a given

26、 2D shell mesh for preform and flow computations. In subsequent papers, we will model finite deformation of preform using the non-linear theory of elasticity, and use this information to model resin flow in an I/C-LCM mo

27、ld.</p><p>　　2. Generating a 3D mesh from the given 2D shell mesh</p><p>　　Our aim is to develop a preprocessor that can generate 3D finite element meshes for flow computations starting from a 2

28、D shell mesh. We wish to allow the I/C-LCM process engineer to include all relevant information such as thicknesses of the layers of the preform, thickness of the gap, into the mesh.</p><p>　　A - open gap ev

29、erywhere C - just touching / partly compressed</p><p>　　D - fully compressed everywhere B - open gap / just touching</p><p>　　Fig. 2. A schematic describing the various stages of the com

30、pression/injection molding process. The top plate of the mold moves along the clamping vector, while the bottom plate is stationary. Stages A–C are three possible starting positions of the top plate. Stage D shows the fi

31、nal configuration of the mold when it is fully compressed.</p><p>　　Fig.2 describes the three possible starting mold configurations (A-C) for a typical angular part geometry. Case A represents the starting c

32、onfiguration for the open mold injection/compression (I/C) molding, with ample gap between the top plate and preform. Cases B and C occur when the gap is partly or completely eliminated before the start of the injection

33、process. In the former, the preform is completely uncompressed with gaps at a few places. In the latter, the gap is removed at the cost of pa</p><p>　　As we shall see in the subsequent papers, six-noded wedg

34、e elements and eight-noded brick elements are adequate for modeling both the resin flow and preform compression. Our mesh generation algorithm is designed to generate such elements from the three- and four-noded triangul

35、ar and quadrilateral elements of the shell mesh.</p><p>　　2.1. Mechanical and flow meshes</p><p>　　Development of the 3D mesh for flow computations from a given 2D shell mesh, representing the p

36、art geometry, is divided into two stages. In the first stage, an intermediate mechanical mesh is created, where the number of layers of elements equals the number of fiber mats in the lay-up, with the thickness of the ma

37、ts equal to the height of those elements. Such a coarse mesh is adequate to track deformation of the mats during compression of the mold. In the second stage, the mechanical mesh is fur</p><p>　　3. Basic con

38、cepts of mesh generation algorithm</p><p>　　We first introduce two basic ideas that form the backbone of our mesh generation algorithm: spines and parallel surfaces.</p><p>　　3.1. Use of spines&

39、lt;/p><p>　　One of the salient features of our mesh generation technique is the use of spines to track the nodes of the 3D mechanical mesh. This is similar to the use of spines in the free boundary problems whe

40、re they have been used to adapt the computational mesh with time. These spines are lines connecting node points of the top mold surface to their counterparts of the bottom mold surface.</p><p>　　4. Algorithm

41、</p><p>　　The main actions carried out in our mesh generation algorithm are as follows:</p><p>　　1. Read data describing the 2D shell mesh. The mesh data is read, along with the information imp

42、ortant for process modeling such as direction of clamping, properties of fiber mats, initial gap provided at the top of the preform. </p><p>　　2. Construct the upper surface of the final part. The upper surf

43、ace is generated parallel to the input 2D shell mesh which represents the bottom, immovable surface of the mold. The input thicknesses between the given and upper surfaces are taken to be the final thickness of the I/C-L

44、CM mold (equal to the desired part thickness).</p><p>　　5. Examples and discussion</p><p>　　A computer program has been developed to implement the mesh generation algorithm, and tested for its e

45、fficacy and robustness. In the following sections, examples of the creation of 3D computational meshes from 2D shell meshes are presented. Since the thicknesses in the I/C-LCM parts are much smaller than their other dime

46、nsions, realistic meshes are relatively thin. To highlight important features of the algorithm, the thicknesses of the meshes are scaled up in the following examples. In each exa</p><p>　　6. Summary and conc

47、lusions</p><p>　　In this paper, we present a methodology to create 3D finite element meshes for modeling mold filling in I/CLCM. We propose the concept of predicting preform compression using the coarse mech

48、anical mesh, and predicting fluid flow using the finer flow mesh. A mesh-generating algorithm, to create the mechanical and flow meshes from a given shell mesh, is presented. This algorithm incorporates information about

49、 the position of fiber mat interfaces in a multi-layered preform, which is crucial for acc</p><p>　　注射／壓縮流體組合模塑的數(shù)值模擬</p><p>　　第一部分 網(wǎng)格生成</p><p>　　K.M. Pillaia, C.L. Tucker III, F.Ra

50、. Phelan Jrb</p><p>　　a伊利諾斯大學(xué)機(jī)械工業(yè)工程系 1206 W. Green Street, Urbana, IL 61801, USA</p><p>　　b國家標(biāo)準(zhǔn)與技術(shù)研究所，聚合物部，聚合物合成組 Building 224, Room B108,Gaithersburg, MD 20899,USA</p><p>　　收稿日期：19

51、99年6月14日</p><p>　　───────────────────────────────────────</p><p><b>　　摘要</b></p><p>　　文章介紹了注入模型中的樹脂在一次初填充后其纖維預(yù)型件被壓縮到所需的程度時(shí)，注射／壓縮流體組合模塑的一種數(shù)值模擬。在多層纖維預(yù)型件中，由于可能存在預(yù)型件頂部的初期間隙以

52、及非平面的不均勻性，有必要進(jìn)行全三維（3D）流體模擬。我們提出一種算法，從描述型腔幾何形狀的二維殼網(wǎng)格開始來生成一個(gè)合適的3D有限元網(wǎng)格。因?yàn)轭A(yù)型件的不同層具有不同的可壓縮性，且滲透性等特性對(duì)壓縮度有很大的作用，因此對(duì)于精密模具填充模擬，有必要對(duì)預(yù)型件隨樹脂流動(dòng)的壓縮率進(jìn)行同步預(yù)報(bào)。此算法建立了一個(gè)粗略的機(jī)械網(wǎng)格來模擬預(yù)型件的壓縮， 以及一個(gè)較好的流體網(wǎng)格來模擬預(yù)型件和間隙中樹脂的運(yùn)動(dòng)。 稱為脊的連接模具上、下模板的管路被用來作為節(jié)點(diǎn)間

53、的通道。一種生成一個(gè)平行于所給曲面的曲面，從而保持中間部的厚度的方法，可用于構(gòu)造機(jī)械網(wǎng)格中預(yù)型件的各層。機(jī)械網(wǎng)格沿著脊進(jìn)一步細(xì)分就建立了流體網(wǎng)格。舉出了由此算法建立三維網(wǎng)格的例子。 1999 Elsevier Science有限公司。版權(quán)所有。</p><p>　　關(guān)鍵詞：流體組合模塑（LCM）； 樹脂傳遞模塑法（RTM）</p><p>　　───────────────────────

54、────────────────</p><p><b>　　1. 引言</b></p><p>　　流體組合模塑（LCM）正在成為一種制造聚合體基質(zhì)合成物網(wǎng)狀零件的重要技術(shù)。 在所有的LCM法中，由加強(qiáng)纖維制成的預(yù)型件被放入閉式壓模中，然后將流體聚合樹脂注入型腔并滲入預(yù)型件。當(dāng)型腔充滿后，聚合物因交聯(lián)反應(yīng)而凝固成為堅(jiān)硬的固體。然后開模取出零件。LCM法提供了一種在低

55、勞動(dòng)需求下用快速加工生產(chǎn)高性能組合零件的方法。</p><p>　　本文討論了LCM法的一種特殊類型，稱為注射／壓縮流體組合模塑（I/C-LCM）。與其它類型的LCM法不同的是，在I/C-LCM中，模具在樹脂注射開始時(shí)是部分閉合的。這樣可以有效增加樹脂流的當(dāng)量面積，且通過提高架構(gòu)的孔隙度降低了流動(dòng)阻力。通常，預(yù)型件頂部間隙的存在更進(jìn)一步增強(qiáng)了流動(dòng)性。所有樹脂注射完畢后，模具慢慢閉合到最終的高度，引起附加的樹脂流動(dòng)

56、并使樹脂滲入預(yù)型件的每一個(gè)部分。比起單獨(dú)采用注射的LCM法（詳情見參考文獻(xiàn)[2]），I/C-LCM法能夠在更低壓力下更快地填充模具。</p><p>　　任何LCM模具設(shè)計(jì)者的主要目的都是用適當(dāng)濕潤的纖維完全填充模型，否則干燥的點(diǎn)造成的不完全填充將導(dǎo)致次品的產(chǎn)生。影響模型填充的幾個(gè)因素有：預(yù)型件的滲透性，模型中間隙的存在促進(jìn)樹脂流動(dòng)，進(jìn)、出口的排列，樹脂從不同入口孔射入的速度，等等。通常模具設(shè)計(jì)者不可能單靠直覺來

57、想象和設(shè)計(jì)一套合適的系統(tǒng)來實(shí)現(xiàn)樹脂的注入，所以常常用模具填充模擬來優(yōu)化模具性能。I/C-LCM中的情形由于充填期間模型的壓縮而比普通的LCM法更為復(fù)雜。因此，在I/C-LCM中運(yùn)用模型填充過程的數(shù)值模擬變得更為重要。</p><p>　　I/C-LCM纖維預(yù)型件通常由多層不同的增強(qiáng)材料組成，如雙晶機(jī)織織物，單晶針腳式接合纖維，任意纖維。每種材料在模型中被壓縮時(shí)都有其獨(dú)特的行為。當(dāng)這些不同的材料被分層形成預(yù)型件時(shí)，

58、隨著模具的閉合各自將受到不同程度的壓縮。這些行為的圖解說明見圖1，它顯示了模型中的一小段。圖中表明隨著模具的閉合，較亮的中心層的變形要大于較暗的外層。</p><p>　　(A) 壓縮前 (B) 壓縮后</p><p>　　圖1 預(yù)型件的各層在壓縮下的不均勻變形</p><p>　　在壓縮期間捕獲這一變形行為是影響I/C-LCM法模型精確度的關(guān)鍵。

59、在壓縮的全過程中樹脂流通過預(yù)型件，所以預(yù)型件的孔隙度和滲透性是決定樹脂流的關(guān)鍵。變形體積與初始體積的比值體現(xiàn)了預(yù)型件每層的孔隙度，且由此可以測(cè)定各層的滲透率，或者也可以從理論預(yù)測(cè)或?qū)嶒?yàn)數(shù)據(jù)的相關(guān)性獲得。對(duì)于I/C-LCM中的模具填充模擬，由于預(yù)型件層的滲透性以及其在壓縮狀態(tài)的強(qiáng)力耦合作用，必須同時(shí)計(jì)算液流和預(yù)型件壓縮率。</p><p>　　在I/C-LCM方法中，已經(jīng)有人對(duì)模具填充的計(jì)算性模擬做了重要的一步。有

60、一種稱為CRIMSON的計(jì)算機(jī)程序可以實(shí)現(xiàn)等溫的模具填充模擬，包括在流動(dòng)范圍內(nèi)同時(shí)計(jì)算液流和預(yù)型件的壓縮率。但是CRIMSON最初只限于二維（2D）平面幾何，對(duì)預(yù)型件壓縮率的預(yù)測(cè)較簡單。由于自由度（DOF)的減少（位移由通常的三個(gè)減少到沿厚度方向的一個(gè)）而能夠?qū)崿F(xiàn)數(shù)學(xué)簡化，預(yù)型件的變形就可根據(jù)增加的線彈性理論模擬。然而典型地由I/C-LCM方法制造的零件都有復(fù)雜的三維外形，這樣就不可能降低數(shù)學(xué)上的復(fù)雜性。目前的這一論文只是描述了我們正提

61、高CRIMSON的能力，使之能夠解決所有任意非平面三維（3D)模型幾何學(xué)問題的努力。</p><p>　　大多數(shù)的注射模塑模擬程序都以殼網(wǎng)格的形式運(yùn)用了模型幾何學(xué)。但是對(duì)于程序工程師來說，即使能夠藉由3D網(wǎng)格來傳達(dá)模型的全部幾何信息，仍然難以將所有信息恰當(dāng)?shù)睾喜?。后者需要知道纖維層各層在各個(gè)時(shí)段的厚度以及相應(yīng)的孔隙度。故以適合單獨(dú)分層區(qū)域的3D有限元網(wǎng)格代表預(yù)型件不同層的單元就十分重要。一個(gè)單元在多個(gè)區(qū)域的重疊不

62、適合傳遞諸如孔隙度、滲透率等僅僅一層纖維層的物料性質(zhì)。達(dá)到最新技術(shù)發(fā)展水平的商用軟件例如PATRAN中的網(wǎng)格生成并非是為生成這樣一個(gè)3D網(wǎng)格而設(shè)計(jì)的。因此，我們決定創(chuàng)建一種適合I/C-LCM模具填充模擬的預(yù)處理程序。</p><p>　　本文的目的是介紹關(guān)于模擬3D I/C-LCM零件模具填充的基本概念，并且提出一種算法，由已知的2D殼網(wǎng)格生成3D有限元網(wǎng)格來實(shí)現(xiàn)預(yù)型件和流體的計(jì)算。在后面的論文中，我們將運(yùn)用非線

63、性彈性理論模擬預(yù)型件的有限長變形，并且用這些信息模擬I/C-LCM模具中的樹脂流動(dòng)。</p><p>　　2. 由已知的2D殼網(wǎng)格生成3D網(wǎng)格</p><p>　　我們的目的是開發(fā)一種由2D殼網(wǎng)格生成用于流體計(jì)算的3D有限元網(wǎng)格的預(yù)處理程序。我們希望讓I/C-LCM程序工程師將所有相關(guān)的信息如預(yù)型件各層厚度、間隙厚度等包含進(jìn)網(wǎng)格之中。</p><p>　　圖2所示為

64、適用于典型有角零件的幾何形狀的初始模型結(jié)構(gòu)。案例A為在頂板和預(yù)型件之間有足夠間隙的明澆注型注射／壓縮（I/C)模塑的初始結(jié)構(gòu)。案例B和C發(fā)生在注射過程開始之前間隙被部分或完全消除之時(shí)。對(duì)于前者，少數(shù)地方的預(yù)型件由于間隙的存在而根本未被壓縮。后者則因預(yù)型件某些區(qū)域的局部壓縮消除了間隙。目前的論文僅僅針對(duì)案例A的網(wǎng)格生成進(jìn)行研究。一旦建立起這一網(wǎng)格，案例B和C就能夠通過解出預(yù)型件的機(jī)械壓力來生成。</p><p>　

65、　正如我們?cè)陔S后的論文中所要見到的，六節(jié)點(diǎn)楔子單元和八節(jié)點(diǎn)塊單元足以用來模擬樹脂流動(dòng)和預(yù)型件的壓縮。我們的網(wǎng)格生成算法正是為了從殼網(wǎng)格中的三節(jié)點(diǎn)和四節(jié)點(diǎn)的三角形以及四邊形單元生成這樣的單元而設(shè)計(jì)的。</p><p>　　A – 各處間隙寬松 C – 恰好接觸／部分壓縮</p><p>　　B – 間隙寬松／恰好接觸 D – 各處完全壓縮</p><

66、p>　　圖2 注射／壓縮模塑過程各種情況的圖解說明。</p><p>　　模具的下模板靜止不動(dòng)，上模板沿夾緊矢量方向移動(dòng)。案例A-C是上模板三種可能初始位置。</p><p>　　案例D所示為模具完全壓縮時(shí)的最終結(jié)構(gòu)。</p><p>　　2.1. 機(jī)械網(wǎng)格和流體網(wǎng)格</p><p>　　由已知的描述零件幾何形狀的2D殼網(wǎng)格產(chǎn)生用于流

67、體計(jì)算的3D網(wǎng)格的研發(fā)分為兩個(gè)階段。在第一階段，建立一個(gè)過渡的機(jī)械網(wǎng)格，其單元層數(shù)等于層疊的纖維層數(shù)，且單元高度等于纖維層的厚度。在模具壓縮期間，這一粗篩足以追蹤纖維層的變形。第二階段，機(jī)械網(wǎng)格沿厚度方向進(jìn)一步細(xì)分而建立更精確的網(wǎng)格，稱為流體網(wǎng)格，用于流體計(jì)算。</p><p>　　3. 網(wǎng)格生成算法的基本概念</p><p>　　我們首先介紹構(gòu)成網(wǎng)格生成算法的主干的兩個(gè)基本概念：脊和平行

68、曲面。</p><p><b>　　3.1. 脊的用途</b></p><p>　　我們的網(wǎng)格生成技術(shù)的一個(gè)特色就是利用脊來跟蹤3D機(jī)械網(wǎng)格的節(jié)點(diǎn)。這有點(diǎn)類似于自由邊界問題中脊的作用，即用來使計(jì)算網(wǎng)格與時(shí)間相適應(yīng)。這些脊都是將上型面的節(jié)點(diǎn)與下型面上相對(duì)的節(jié)點(diǎn)相連接的線條。</p><p><b>　　4. 算法</b>&l

69、t;/p><p>　　網(wǎng)格生成算法實(shí)現(xiàn)的主要功能如下：</p><p>　　1. 讀取描述2D殼網(wǎng)格的數(shù)據(jù)。讀取網(wǎng)格數(shù)據(jù)，包括諸如夾緊方向、纖維層性質(zhì)、預(yù)型件頂部的初始間隙等對(duì)加工模擬很重要的信息。</p><p>　　2. 構(gòu)造最終零件的上表面。. 上表面是平行于輸入的2D網(wǎng)格而生成的，該網(wǎng)格描述了模具下面不動(dòng)的面。輸入的已知表面和上表面之間的厚度應(yīng)為I/C-LCM模

70、具最終的厚度（等于想要得到的零件的厚度）。</p><p><b>　　5. 示例及討論</b></p><p>　　我們開發(fā)了一套計(jì)算機(jī)程序來實(shí)現(xiàn)網(wǎng)格生成算法，并檢驗(yàn)了它的功效和耐用性。下面的章節(jié)將提出一個(gè)由2D殼網(wǎng)格建立3D計(jì)算網(wǎng)格的例子。因?yàn)镮/C-LCM零件的厚度遠(yuǎn)小于其他尺寸，實(shí)際的網(wǎng)格將相應(yīng)變薄。但為了突出算法的重要特點(diǎn)，在下面的舉例中網(wǎng)格厚度將按比例擴(kuò)大

71、。在每個(gè)例子中，規(guī)定預(yù)型件的上表面和上模板之間的間隙為未被壓縮的預(yù)型件總厚度的某一部分。</p><p><b>　　6. 總結(jié)和結(jié)論</b></p><p>　　在本文中，我們提出了建立3D有限元網(wǎng)格用于在I/C-LCM中模擬模具填充的一套方法。我們主張，利用粗略的機(jī)械網(wǎng)格預(yù)測(cè)預(yù)型件的壓縮率，并用更好的流體網(wǎng)格來預(yù)測(cè)流體流動(dòng)。提出一種網(wǎng)格生成算法，由已知的殼網(wǎng)格來建

72、立機(jī)械和流體網(wǎng)格。此算法結(jié)合多層預(yù)型件中有關(guān)纖維層分界面位移的信息，對(duì)于填充過程的精確模擬至關(guān)重要。一種平行于任意殼網(wǎng)格的曲面來建立曲面的技術(shù)，使我們能夠精確地描述分界面。此外，在網(wǎng)格生成中使用脊，使每個(gè)節(jié)點(diǎn)的未知量由三個(gè)減少到一個(gè)。使用這一算法，我們成功地由兩個(gè)不同的殼網(wǎng)格建立了機(jī)械和流體網(wǎng)格，能由殼網(wǎng)格建立任意模型形狀的3D網(wǎng)格顯示了它的實(shí)用性。此算法主要的局限在于，需要在模具厚度逐步改變的區(qū)域改善殼網(wǎng)格。在后面的論文中，我們將利用